On the soliton-type and other physical solutions for the space–time fractional Kraenkel–Manna–Merle model

Abstract

The space–time fractional Kraenkel–Manna–Merle system (FKMMS) is a mathematical physics system that is particularly established to outline the transmission of nonlinear short waves in ferromagnetic materials considering the impact of a zero conductivity external field. Motivated by this application, the current investigation seeks to thoroughly examine the space–time FKMMS with conformable fractional derivatives. Generalised EDAM (gEDAM), an improved variant of the modified extended direct algebraic method (EDAM), is utilised to efficiently find a collection of analytical travelling wave solutions in the form of rational, hyperbolic, exponential and trigonometric functions. Through a careful selection of particular values for the parameters associated with the arbitrary functions contained in the obtained solutions, the inferred solutions yield various new forms for travelling waves and other soliton-type structures. Within the scope of FKMMS, our analytical investigation identified many kink solitons, including kink, anti-kink, bell-shaped dark and brilliant kink. An analysis is conducted on the effects of several factors associated with the obtained solutions, including the space- and time-fractional parameters on the shock and solitary wave profiles. This work may provide critical new understandings for researchers, engineers and physicists working with ferromagnetic materials. Regarding the real-world occurrences seen throughout their experimental research, it can offer helpful insights.